By Lisa Mascaro

Tribune Washington Bureau

WASHINGTON, D.C. — Senate Republicans reconvened behind closed doors Wednesday trying to break the impasse on their health care overhaul but emerged with no apparent strategy for resolving differences by an end-of-week deadline.

Senate Majority Leader Mitch McConnell of Kentucky vowed to try again for a vote after the Fourth of July recess, despite having abruptly delayed action this week.

Senators were aiming for a revised bill by Friday, the Republican Whip, Sen. John Cornyn of Texas, told reporters, so it could be assessed by the Congressional Budget Office during the break.

But senators remained skeptical after the lengthy lunchtime huddle that appeared to run long on ideas but short on consensus.

“I think it’s going to be very difficult,” said Sen. Susan Collins, R-Maine.

McConnell surprised senators by delaying this week’s expected votes once it became clear he did not have a majority for passage — or possibly to even open the debate.

As many as 10 Republican senators now publicly oppose the bill, the Better Care Reconciliation Act, and leaders are scrambling to win them over with an estimated $200 billion in savings from the bill that can be applied to their particular state’s needs.

But even with that fund of resources, it is not clear McConnell will be able to satisfactorily improve the legislation, which now threatens to cut 22 million Americans off health insurance. He can only afford to lose two Republican votes in the face of Democratic opposition.

“It’s going to be very difficult to get me to a yes … have to make us an offer we can’t refuse,” Sen. Dean Heller, R-Nev., said on a telephone town hall late Tuesday, according to journalist Jon Ralston, who monitored the call.

Fresh polling Wednesday showed paltry support for the Republican approach to overhauling the Affordable Care Act, known as Obamacare, which has enjoyed a surge in popularity now that Republicans are closer than ever to repealing it. A USA Today poll put approval of the Senate GOP bill at 12 percent.

Republicans, though, are under enormous pressure from their most conservative supporters — and big dollar donors, including the powerful Koch network — to deliver on their promised to end Obamacare.

Senate Democrats, meanwhile, suggested that President Donald Trump convene all 100 senators — much the way then-President Barack Obama did during his first days in office for a session at Blair House — to see how they might be able to work together to improve, rather than repeal, the Affordable Care Act.

“I’d make my friends on the Republican side and President Trump an offer: Let’s turn over a new leaf. Let’s start over,” said Senate Minority Leader Charles E. Schumer, D-N.Y.

“President Trump, I challenge you to invite us — all 100 of us, Republican and Democrat — to Blair House to discuss a new bipartisan way forward on health care in front of all the American people.”

No such invitation, however, seemed forthcoming. Trump dismissed Schumer’s proposal — “he just doesn’t seem like a serious person,” the president said — and instead promised his own “big surprise” on health care.

“Health care is working along very well,” Trump told reporters at the White House. “We could have a big surprise, with a great health care package.”

Asked what he meant by a big surprise, Trump simply repeated: “A great, great surprise.”

The Republican bill, like its counterpart passed by House Republicans, does not fully gut Obamacare, but rescinds the new taxes imposed on high-income individuals and health care companies to pay for expanding coverage through Medicaid and subsidies for private insurance on the ACA marketplace.

Senators said the private talks Wednesday focused mainly on changes to the Obamacare marketplace that could bring down the cost of insurance premiums.

One idea from Sen. Ted Cruz, R-Texas, to allow insurers to offer policies that do not meet the Obamacare benchmarks for what insurance needs to cover met with mixed reaction, senators said.

Sen. Bill Cassidy, a physician, warned that such changes would alter the risk pool, keeping insurance costs high.

“You end up with policies that, for example, don’t cover maternity,” Cassidy said. “Do you want a policy that doesn’t have maternity, which would be principally appealing to young men, when obviously typically men have had a role in that pregnancy?”

Other senators were floating new ideas, but McConnell gave no indication whether those proposals would be included in the final revised product.